Computation of symbolic dynamics for one-dimensional maps

Autor:	Pieter Collins, Lorenzo Sella
Přispěvatelé:	Scientific Computing
Rok vydání:	2010
Předmět:	Kneading theory Van der Pol oscillator Applied Mathematics Computation Symbolic dynamics Disjoint sets Symbolic computation Interval arithmetic Computational Mathematics Symbolic trajectory evaluation One-dimensional map Entropy (information theory) Algorithm Mathematics
Zdroj:	Journal of Computational and Applied Mathematics, 234, 418-436
ISSN:	0377-0427
DOI:	10.1016/j.cam.2009.12.034
Popis:	In this paper we design and implement rigorous algorithms for computing symbolic dynamics for piecewise-monotone-continuous maps of the interval. The algorithms are based on computing forwards and backwards approximations of the boundary, discontinuity and critical points. We explain how to handle the discontinuities in the symbolic dynamics which occur when the computed partition element boundaries are not disjoint. The method is applied to compute the symbolic dynamics and entropy bounds for the return map of the singular limit of a switching system with hysteresis and the forced Van der Pol equation.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_dedup___::458375090cec451a63293480a9358e4d https://doi.org/10.1016/j.cam.2009.12.034 Zobrazit plný text záznamu Full Text from ScienceDirect